A Generic Complete Dynamic Logic for Reasoning About Purity and Effects

  • Till Mossakowski
  • Lutz Schröder
  • Sergey Goncharov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4961)

Abstract

For a number of programming languages, among them Eiffel, C, Java and Ruby, Hoare-style logics and dynamic logics have been developed. In these logics, pre- and postconditions are typically formulated using potentially effectful programs. In order to ensure that these pre- and postconditions behave like logical formulae (that is, enjoy some kind of referential transparency), a notion of purity is needed. Here, we introduce a generic framework for reasoning about purity and effects. Effects are modeled abstractly and axiomatically, using Moggi’s idea of encapsulation of effects as monads. We introduce a dynamic logic (from which, as usual, a Hoare logic can be derived) whose logical formulae are pure programs in a strong sense. We formulate a set of proof rules for this logic, and prove it to be complete with respect to a categorical semantics. Using dynamic logic, we then develop a relaxed notion of purity which allows for observationally neutral effects such writing on newly allocated memory.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Till Mossakowski
    • 1
    • 2
  • Lutz Schröder
    • 1
    • 2
  • Sergey Goncharov
    • 2
  1. 1.DFKI LaboratoryBremen
  2. 2.Department of Computer ScienceUniversity of Bremen 

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